mlsanityData to 7 Oct 2026

Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior

arXiv 1811.09558 ↗First posted 23 Nov 2018cs.LG cs.AI stat.MLcited by 31

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Abstract (arXiv)

Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and probability of improvement achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Nov 2018.

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Citing papers per year: 2021: 3; 2022: 11; 2023: 6; 2024: 5; 2025: 4; 2026: 2.

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  1. 2022Towards Learning Universal Hyperparameter Optimizers with Transformerscited by 81
  2. 2021Pre-trained Gaussian Processes for Bayesian Optimizationcited by 63
  3. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
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  5. 2023Transfer Learning for Bayesian Optimization: A Surveycited by 27
  6. 2023Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Boundscited by 15
  7. 2021Open Problem: Tight Online Confidence Intervals for RKHS Elementscited by 13
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  9. 2023Transfer Learning for Bayesian Optimization on Heterogeneous Search Spacescited by 9
  10. 2022On Provably Robust Meta-Bayesian Optimizationcited by 8
  11. 2022Collaborative Learning in Kernel-based Bandits for Distributed Userscited by 6
  12. 2024Bayesian Optimisation with Unknown Hyperparameters: Regret Bounds Logarithmically Closer to Optimalcited by 6
19 more
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  5. 2023A Scalable Test Problem Generator for Sequential Transfer Optimizationcited by 5
  6. 2022HPC Storage Service Autotuning Using Variational-Autoencoder-Guided Asynchronous Bayesian Optimizationcited by 4
  7. 2022HyperBO+: Pre-training a universal prior for Bayesian optimization with hierarchical Gaussian processescited by 4
  8. 2022Lifelong Bandit Optimization: No Prior and No Regretcited by 3
  9. 2023Rover: An online Spark SQL tuning service via generalized transfer learningcited by 3
  10. 2024A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcited by 3
  11. 2026ProEval: Proactive Failure Discovery and Efficient Performance Estimation for Generative AI Evaluationcited by 2
  12. 2024An Adaptive Dimension Reduction Estimation Method for High-dimensional Bayesian Optimizationcited by 1
  13. 2025Provable Accelerated Bayesian Optimization with Knowledge Transfercited by 1
  14. 2025Robust Bayesian Optimisation with Unbounded Corruptionscited by 1
  15. 2023Generalization within in silico screeningcited by 0
  16. 2024Few-shot Scooping Under Domain Shift via Simulated Maximal Deployment Gapscited by 0
  17. 2024Sample-Efficient Bayesian Optimization with Transfer Learning for Heterogeneous Search Spacescited by 0
  18. 2025Clustering-based Meta Bayesian Optimization with Theoretical Guaranteecited by 0
  19. 2026Online Sharp-Calibrated Bayesian Optimizationcited by 0